throughout the motion, T/v is constant and dQ＝JCpNmdT, whence
| Cp＝12(n+5) R/Jm. | (20) |
By division of the values of Cp and Cv, , we find for γ, the ratio of the specific heats.
| γ＝1 +2/n+3). | (21) |
The comparison of this formula with experiment provides a striking confirmation of the truth of the kinetic theory but at the same time discloses the most formidable difficulty which the theory has so far had to encounter.
On giving different values to n in formula (21), we obtain the values for γ:
| n ＝ | 0, | 1, | 2, | 3, | 4, | 5, | |
| γ ＝ | 1·66, | 1·5, | 1·4, | 1·33, | 1·28, | 1·25, | &c. |
Thus, to within the degree of approximation to which our theory is accurate, the value of γ for every gas ought to be one of this series. The following are the values of γ for gases for which γ can be observed with some accuracy:—
| Mercury | 1·66 | Nitrogen | 1·40 |
| Krypton | 1·66 | Carbon monoxide | 1·41 |
| Helium | 1·65 | Hydrogen | 1·40 |
| Argon | 1·62 | Oxygen | 1·40 |
| Air | 1·40 | Hydrochloric acid | 1·39 |
It is clear that for the first four gases n＝0, while for the remainder n＝2. To examine what is meant by a zero value of n we refer to formula (15). The value of n is the number of terms in the energy of the molecule beyond that due to translation. Thus when n＝0, the whole energy must be translational: there can be no energy of rotation or of internal motion. The molecules of gases for which n＝0 must accordingly be spherical in shape and in internal structure, or at least must behave at collisions as though they were spherical, for they would otherwise be set into rotation by the forces experienced at collisions. In the light of these results it is of extreme significance that the four gases for which n＝0 are all believed to be monatomic: the molecules of these gases consist of single atoms. Moreover, these four are the only monatomic gases for which the value of γ is known, so that the only atoms of which the shape can be determined are found to be spherical. It is at least a plausible conjecture, until the contrary is proved, that the atoms of all elements are spherical.[1]
The next value which occurs is n＝2. The kinetic energy of the molecules of these gases must contain two terms in addition to those representing translational energy. For a rigid body the kinetic energy will, in general, consist of three terms (Aω12+Bω22+Cω32) in addition to the translational energy. The value n＝2 is appropriate to bodies of which the shape is that of a solid of revolution, so that there is no rotation about the axis of symmetry. We must accordingly suppose that the molecules of gases for which n＝2 are of this shape. Now this is exactly the shape which we should expect to find in molecules composed of two spherical atoms distorting one another by their mutual forces, and all gases for which n＝2 are diatomic.
No molecule could possibly be imagined for which n had a negative value or the value n＝1. The theory therefore passes a crucial test when it is discovered that no gases exist for which n is either negative or unity. On the other hand, the theory encounters a very serious difficulty in the fact that all molecules possess a great number of possibilities of internal motion, as is shown by the number of distinct lines in their spectra both of emission and of absorption. So far as is known, each line in the spectrum of, say, mercury, represents a possibility of a distinct vibration of the mercury atom, and accordingly provides two terms (say αφ2+βφ2, where φ is the normal co-ordinate of the vibration) in the expression for the energy of the molecule. There are many thousands of lines in the mercury spectrum, so that from this evidence it would appear that for mercury vapour n ought to be very great, and γ almost equal to unity. Instead of this we have n＝0, and γ=123 . As a step towards removing this difficulty we notice that the energy of a vibration such as is represented by a spectral line has the peculiarity of being unable to exist (so far as we know) without suffering dissipation into the ether. This energy, therefore, comes under a different category from the energy for which the law of equipartition was proved, for in proving this law conservation of energy was assumed. The difficulty is further diminished when it is proved, as it can be proved,[2] that the modes of energy represented in the atomic spectrum acquire energy so slowly that the atom might undergo collisions with other atoms for centuries before being set into oscillations which would possess an appreciable amount of energy. In fact the proved tendency for the gas to pass into the “normal state” in which there is equipartition of energy, represents in this case nothing but the tendency for the translational energy to become dissipated into the energy of innumerable small vibrations. We find that this dissipation, although undoubtedly going on, proceeds with extreme slowness, so that the vibrations pass their energy on to the ether as rapidly as they acquire it, and the “normal state” is never established. These considerations suggest that the difficulty which has been pointed out may be apparent rather than real. At the same time this difficulty is only one aspect of a wider difficulty which cannot be lightly passed over; Maxwell himself regarded it as the principal obstacle in the way of the full acceptance of the theory of which he was so largely the author. (J. H. Je.)
MOLE-RAT, the name of a group of blind burrowing rodents, typified by the large grey Spalax typhlus of eastern Europe and Egypt, which represents the Old World family Spalacidae.
All the mole-rats of the genus Spalax are characterized by the
want of distinct necks, small or rudimentary ears and eyes,
and short limbs provided with powerful digging claws. There
are three pairs of cheek-teeth which are rooted, and show folds
of enamel on the crown. Mole-rats are easily recognized by the
peculiarly flattened head, in which the minute eyes are covered
with skin, the wart-like ears, and rudimentary tail; they make
burrows in sandy soil, and feed on bulbs and roots. Bamboo-rats,
of which one genus (Rhizomys) is Indian and Burmese, and
the other (Tachyoryctes) East African, differ by the absence of
skin over the eyes, the presence of short ears, and a short,
sparsely-haired tail. They burrow either among tall grass,
or at the roots of trees (see Rodentia).
MOLE-SHREW, any individual of the genera Urotrichus and Uropsilus (see Insectivora). These animals, which are sometimes called shrew-moles, are not moles with shrew-like habits, but shrews with the burrowing habits of moles and resembling them in appearance.
MOLESKIN, a term employed not only for the skin of a mole but also, from a real or fancied resemblance, for a stout heavy cotton fabric of leathery consistence woven as a satin twill on a
strong warp. It is shorn before being dyed or bleached. Being
of an exceedingly durable and economical texture, it has been
much worn by working-men, especially outdoor labourers. It
is also used for gun-cases, carriage-covers, and several purposes
in which a fabric capable of resisting rough usage is desirable.
MOLESWORTH, MARY LOUISA (1839–), Scottish
writer, daughter of Major-General Stewart, of Strath, N.B., was born in Rotterdam on the 29th of May 1839, and was educated in Great Britain and abroad. In. 1861 Miss Stewart married Major R. Molesworth. Her first novels, Lover and Husband (1869) to Cicely (1874), appeared under the pseudonym of “Ennis Graham.” Mrs Molesworth is best known as a writer of books for the young, such as Tell Me a Story (1875), Carrots (1876), and The Cuckoo Clock (1877).
MOLESWORTH, ROBERT MOLESWORTH, 1st Viscount
(1656–1725), came of an old Northamptonshire family. His
father Robert (d. 1656) was a Cromwellian who made a fortune in Dublin, and he himself supported William of Orange and in 1695 became a prominent member of the Irish privy council. In 1716 he was created a viscount. He was succeeded by his two sons, John, 2nd viscount (1679–1726), and Richard 3rd viscount (1680–1758), the latter of whom saved Marlborough’s life at the battle of Ramillies and rose to be a field-marshal. The 3rd viscount’s son Richard Nassau (1748–1793) succeeded
to the title, which has descended accordingly.
A great-grandson of the 1st viscount, John Edward Nassau Molesworth (1790–1877), vicar of Rochdale, was a well-known High Churchman and controversialist; and two of his sons became prominent men—William Nassau Molesworth (1816–1890), author of History of England 1830–1871 (1871–1873), History of the Reform Bill (1865), and History of the Church of
- ↑
Very significant confirmation of this conjecture is obtained
from a study of the specific heats of the elements in the solid
state. If a solid body is regarded as an aggregation of similar atoms
each of mass m, its specific heat C is given, as in formula (19) by
C＝12(n+3)R/Jm. From Dulong and Petit’s law that Cm is the same
for all elements, it follows that n+3 must be the same for all atoms.
Moreover, the value of Cm shows that n+3 must be equal to six.
Now if the atoms are regarded as points or spherical bodies oscillating
about positions of equilibrium, the value of n+3 is precisely six,
for we can express the energy of the atom in the form
E＝12(mu2+mv2+mw2+x2∂2V∂x2 + y2∂2V∂y2 + z2∂2V∂z2),
where V is the potential and x, y, z are the displacements of the atom referred to a certain set of orthogonal axes.
- ↑ J. H. Jeans, Dynamical Theory of Gases, ch. ix.
